ABSTRACT
This paper presents a novel application of percolation theory for the development of a three-dimensional two-phase waterflood model.
The waterflood model consists of a three-dimensional, two-phase cubic reservoir composed of many smaller cells. The model represents one-quarter of a five spot waterflood pattern and has one injection well at one corner and a production well at the opposite corner.
Two different random numbers are allocated to each cell throughout the lattice. Based upon the first random number, one decides upon the contents of the cell (oil or water). The permeability of that cell is determined from the second random number, which belongs to a log-normal distribution density. The lattice is swept cell by cell with the displacing fluid (water) following certain invasion rules. The model stores the oil and water clusters (aggregates) as well as the fluid production. The simulated waterflood process terminates when no more oil is produced. Then the residual oil saturation (trapped oil) is computed and the spatial location in the lattice is printed (graphed). These simulations were done on a CRAY Y-MP2/116 Supercomputer using vectorized code.
Several characteristics of this model were investigated: First, the effect upon the residual oil saturation of different initial water saturations; second, the effects of fluid allocation by using different probability distribution functions, i.e. uniform, normal, and Beta distribution densities; third, the effect of different parameters in the log-normal distribution for permeabilities to indicate different degrees of heterogeneity of the porous media; and last, the effect of lattice size upon the residual oil saturation. The results are encouraging, and we envision that the model could be extended to layered reservoirs.
